Interference alignment (IA) has been well recognized as a promising technique to obtain large multiplexing gain in multiple input multiple output (MIMO) interference channels. Most of the existing IA schemes require global channel state information (CSI) at the transmitter to design precoding vectors, which causes high amount of feedback bits. To reduce the feedback overhead, in this paper, we investigate the IA scheme employing differential CSI feedback over time-correlated MIMO channels. Specifically, we analyze the achievable sum-rate performance, and derive the minimum differential feedback rate to preserve the maximum multiplexing gain. In addition, we use the general alternating-minimization precoder design scheme to verify the analytical results.